We will have to use the distance formula in order to determine the lengths of each side of the triangle.
Distance formula:
Let's calculate AB first:
A (1, 7) and B (-2, 2)
A: x1 = 1 and y1 = 7
B: x2 = -2 and y2 = 2
so
AB =
or (rounded to the nearest tenth) ≈ 5.8
Now let's do BC:
B: x1 = -2 and y1 = 2
C: x2 = 4 and y2 = 2
So
BC =
or 6
Now let's do CA
C: x1 = 4 and y1 = 2
A: x2 = 1 and y2 = 7
So
CA =
or (rounded to the nearest tenth) ≈ 5.8
So let's recap:
AB ≈ 5.8
BC = 6
CA ≈ 5.8
So AB and AC are the same length while BC is .2 units longer which means this is an isosceles triangle.
Distance formula:
Let's calculate AB first:
A (1, 7) and B (-2, 2)
A: x1 = 1 and y1 = 7
B: x2 = -2 and y2 = 2
so
AB =
Now let's do BC:
B: x1 = -2 and y1 = 2
C: x2 = 4 and y2 = 2
So
BC =
Now let's do CA
C: x1 = 4 and y1 = 2
A: x2 = 1 and y2 = 7
So
CA =
So let's recap:
AB ≈ 5.8
BC = 6
CA ≈ 5.8
So AB and AC are the same length while BC is .2 units longer which means this is an isosceles triangle.